Course: MTH 111/Pre-Calculus A Teacher: Ameena Amdahl-Mason Duration: 1 term (0.5 credit if taken for high school credit alone) Articulation: 4 college credits will be awarded for an A or a B Textbook:Algebra and Trigonometry with Modeling and Visualization, 3rd ed., Gary Rockswold, Pearson/Addison Wesley.
Course Description
This course is part I of a pre-calculus sequence that provides an extensive study of functions and their inverses modeled algebraically, numerically and graphically. Specific functions include the exponential, logarithmic, polynomial and power functions. Modeling real world applications are emphasized.
Course Objectives
This course will foster an understanding of functions and their properties, including rates of change, short- and long-run behavior, transformations and symmetry, algebra and composition of functions, inverse functions, discrete functions, and fitting functions to data. Particular attention will be paid to the use of functions to model applications and solve problems.
Attendance Policy
Students are expected to attend every class. If a student misses a class, it is his or her responsibility to ask for assignments and make up the work. Any missed tests or quizzes must be rescheduled within 24 hours of returning from an absence.
Grading Rubric
Homework = 25 %
Tests = 55 %
Final = 10 % Specific Learning Outcomes
The student will be able to:
· Define and identify functions using each method from the rule of four.
· Read and write function notation as a means of communication.
· Compute and interpret the average rate of change of a function over an interval.
· Determine the short-run behavior of a function.
· Determine the long-run behavior of a function.
· Construct linear functions to model applications.
· Fit linear functions to data sets.
· Determine an appropriate domain and range for a function.
· Read and write formulas for, and model applications using piecewise-defined functions.
· Determine and describe the concavity of a function.
· Define and identify an exponential function.
· Construct exponential functions to model applications.
· Fit exponential functions to data sets.
· Use the natural exponential function to model applications.
· Define and identify a logarithmic function.
· Construct logarithmic functions to model applications.
· Fit logarithmic functions to data sets.
· Use the natural logarithmic function to model applications.
· Use the properties of logarithms to solve equations.
· Identify rigid transformations of elementary functions.
· Identify non-rigid transformations of elementary functions.
· Determine symmetries of a function.
· Define and compute the composition of functions.
· Perform the algebra associated with the composition of functions.
· Determine if a function is invertible.
· Find the inverse of an invertible function.
· Compare the domain and range of a function with those of its inverse.
· Define and identify polynomial functions.
· Use polynomial functions to model applications.
· Define and identify rational functions.
· Use rational functions to model applications
· Compare and contrast linear, exponential, logarithmic, polynomial, and rational functions.
· Define and identify discrete functions.
· Compare and contrast arithmetic and geometric sequences.
· Define and identify series.
· Compute the sum of an arithmetic series.
· Compute the sum of a finite geometric series.
· Determine when an infinite geometric series converges.
· Compute the sum of a convergent infinite geometric series.
· Model and solve applications using sequences and series.
· Demonstrate rigorous and analytical thinking by reading, writing, and utilizing the technical and logical language and symbolism necessary to do mathematics and to solve problems effectively and efficiently.
· Work effectively as a team member to engage in problem solving.
Teacher: Ameena Amdahl-Mason
Duration: 1 term (0.5 credit if taken for high school credit alone)
Articulation: 4 college credits will be awarded for an A or a B
Textbook: Algebra and Trigonometry with Modeling and Visualization, 3rd ed., Gary Rockswold, Pearson/Addison Wesley.
Course Description
This course is part I of a pre-calculus sequence that provides an extensive study of functions and their inverses modeled algebraically, numerically and graphically. Specific functions include the exponential, logarithmic, polynomial and power functions. Modeling real world applications are emphasized.
Course Objectives
This course will foster an understanding of functions and their properties, including rates of change, short- and long-run behavior, transformations and symmetry, algebra and composition of functions, inverse functions, discrete functions, and fitting functions to data. Particular attention will be paid to the use of functions to model applications and solve problems.
Attendance Policy
Students are expected to attend every class. If a student misses a class, it is his or her responsibility to ask for assignments and make up the work. Any missed tests or quizzes must be rescheduled within 24 hours of returning from an absence.
Grading Rubric
Homework = 25 %
Tests = 55 %
Final = 10 %
Specific Learning Outcomes
The student will be able to:
· Define and identify functions using each method from the rule of four.
· Read and write function notation as a means of communication.
· Compute and interpret the average rate of change of a function over an interval.
· Determine the short-run behavior of a function.
· Determine the long-run behavior of a function.
· Construct linear functions to model applications.
· Fit linear functions to data sets.
· Determine an appropriate domain and range for a function.
· Read and write formulas for, and model applications using piecewise-defined functions.
· Determine and describe the concavity of a function.
· Define and identify an exponential function.
· Construct exponential functions to model applications.
· Fit exponential functions to data sets.
· Use the natural exponential function to model applications.
· Define and identify a logarithmic function.
· Construct logarithmic functions to model applications.
· Fit logarithmic functions to data sets.
· Use the natural logarithmic function to model applications.
· Use the properties of logarithms to solve equations.
· Identify rigid transformations of elementary functions.
· Identify non-rigid transformations of elementary functions.
· Determine symmetries of a function.
· Define and compute the composition of functions.
· Perform the algebra associated with the composition of functions.
· Determine if a function is invertible.
· Find the inverse of an invertible function.
· Compare the domain and range of a function with those of its inverse.
· Define and identify polynomial functions.
· Use polynomial functions to model applications.
· Define and identify rational functions.
· Use rational functions to model applications
· Compare and contrast linear, exponential, logarithmic, polynomial, and rational functions.
· Define and identify discrete functions.
· Compare and contrast arithmetic and geometric sequences.
· Define and identify series.
· Compute the sum of an arithmetic series.
· Compute the sum of a finite geometric series.
· Determine when an infinite geometric series converges.
· Compute the sum of a convergent infinite geometric series.
· Model and solve applications using sequences and series.
· Demonstrate rigorous and analytical thinking by reading, writing, and utilizing the technical and logical language and symbolism necessary to do mathematics and to solve problems effectively and efficiently.
· Work effectively as a team member to engage in problem solving.
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